A continuous model of angiogenesis: initiation, extension, and maturation of new blood vessels modulated by vascular endothelial growth factor, angiopoietins, platelet-derived growth factor-B, and pericytes.

This work presents a continuous model for three early stage events in angiogenesis: initiation, sprout extension, and vessel maturation. We care- fully examine the regulating mechanisms of vascular endothelial growth factor (VEGF) and angiopoietins (Ang1 and Ang2) on the proliferation, migration and maturation of endothelial cells through their endothelium-specific receptor tyrosine kinase VEGFR2 and Tie2, respectively. We also consider the effect of platelet-derived growth factor-B (PDGF-B) on the proliferation and migration of pericytes. For growth factors, we present a mathematical model integrating molecular reactions on blood vessels with tissue-level diffusion. For capillary extension, we develop a visco-elastic model to couple tip cell protrusion, en- dothelium elasticity, and stalk cell proliferation. Our model reproduces corneal angiogenesis experiments and several anti-angiogenesis therapy results. This model also demonstrates that (1) the competition between Ang1 and Ang2 is the angiogenic switch; (2) the maturation process modulated by pericytes and angiopoietins is crucial to vessel normalization and can explain the resistance to anti-VEGF therapy; (3) combined anti-pericyte and anti-VEG